Question: Which of the following numbers is a multiple of 11? ${44,58,71,97,119}$
The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $44 \div 11 = 4$ $58 \div 11 = 5\text{ R }3$ $71 \div 11 = 6\text{ R }5$ $97 \div 11 = 8\text{ R }9$ $119 \div 11 = 10\text{ R }9$ The only answer choice that leaves no remainder after the division is $44$ $ 4$ $11$ $44$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $44$ $44 = 2\times2\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $44$. We can say that $44$ is divisible by $11$.